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STOCHASTIC MODELS OF SATURN’S PLANETARY MAGNETIC FIELD
by
Marcia Richardson
A Thesis Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
MASTER OF SCIENCE
(GEOLOGICAL SCIENCES)
December 2008
Copyright 2008 Marcia Richardson

We have calculated new models of Saturn's internal planetary magnetic field based on a stochastic inversion technique. The stochastic inversion technique is used to identify a model that is a compromise between a solution that fits the data well by minimizing the error and one that provides the simplest solution, obtained by minimizing a smoothing norm or physical constraint that incorporates prior information based on knowledge of the physics of the problem. We find models that fit the data using the mean square field strength or radial field at the surface as the smoothing norm or constraint on the magnetic field structure. Since there is no consensus regarding Saturn's rotation period, we calculate models based on two proposed periods, 10 hours 47 minutes 6 seconds determined from a periodic signature in the magnetic field and 10 hours 32 minutes 35 seconds determined by use of gravity and wind data. We find that models based on the shorter rotation period yield implausible physical characteristics, such as regions of radially outward field in the southern hemisphere which is not seen in the data and exceptionally large values of the surface field magnitude. We conclude that this rotation period is unlikely to represent the rotation rate of the deep interior. We have also derived models based on the generalized inverse techniques that have previously been applied to the outer planets. Both types of models fit the data well, with mean values of the root-mean-square misfit from 1.7 - 1.74 nT, approximately .01% of the surface field magnitude. The models based on stochastic inversion are characterized by much larger non-axial model coefficients than those based on the generalized inverse technique. The general characteristics of Saturn's planetary magnetic field are calculated based on the stochastic models.; The magnetic dipole ranges from 4.62 - 4.64 x 10^18Tm^3 the tilt angle of the dipole axis ranges from 0.22 -0.25 degrees and the northward displacement of the magnetic equator is 0.037 Rs. We also evaluate the harmonic content and symmetry properties of the model in the context of mean-field dynamo theory.

STOCHASTIC MODELS OF SATURN’S PLANETARY MAGNETIC FIELD
by
Marcia Richardson
A Thesis Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
MASTER OF SCIENCE
(GEOLOGICAL SCIENCES)
December 2008
Copyright 2008 Marcia Richardson